Delta-Nabla Optimal Control Problems

We present a unified treatment to control problems on an arbitrary time scale by introducing the study of forward-backward optimal control problems. Necessary optimality conditions for delta-nabla isoperimetric problems are proved, and previous results in the literature obtained as particular cases. As an application of the results of the paper we give necessary and sufficient Pareto optimality conditions for delta-nabla bi-objective optimal control problems.Comment: Preprint version of an article submitted 28-Nov-2009; revised 02-Jul-2010; accepted 20-Jul-2010; for publication in Journal of Vibration and Contro

Euler-Lagrange equations for composition functionals in calculus of variations on time scales

In this paper we consider the problem of the calculus of variations for a functional which is the composition of a certain scalar function $H$ with the delta integral of a vector valued field $f$, i.e., of the form $H(\int_{a}^{b}f(t,x^{\sigma}(t),x^{\Delta}(t))\Delta t)$. Euler-Lagrange equations, natural boundary conditions for such problems as well as a necessary optimality condition for isoperimetric problems, on a general time scale, are given. A number of corollaries are obtained, and several examples illustrating the new results are discussed in detail.Comment: Submitted 10-May-2009 to Discrete and Continuous Dynamical Systems (DCDS-B); revised 10-March-2010; accepted 04-July-201

A General Backwards Calculus of Variations via Duality

We prove Euler-Lagrange and natural boundary necessary optimality conditions for problems of the calculus of variations which are given by a composition of nabla integrals on an arbitrary time scale. As an application, we get optimality conditions for the product and the quotient of nabla variational functionals.Comment: Submitted to Optimization Letters 03-June-2010; revised 01-July-2010; accepted for publication 08-July-201

Direct and Inverse Variational Problems on Time Scales: A Survey

We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to attain a local minimum at a given point of the vector space. Furthermore, we provide a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation (Helmholtz's problem of the calculus of variations on time scales). New and interesting results for the discrete and quantum settings are obtained as particular cases. Finally, we consider very general problems of the calculus of variations given by the composition of a certain scalar function with delta and nabla integrals of a vector valued field.Comment: This is a preprint of a paper whose final and definite form will be published in the Springer Volume 'Modeling, Dynamics, Optimization and Bioeconomics II', Edited by A. A. Pinto and D. Zilberman (Eds.), Springer Proceedings in Mathematics & Statistics. Submitted 03/Sept/2014; Accepted, after a revision, 19/Jan/201

On finite pp-groups whose automorphisms are all central

An automorphism $\alpha$ of a group $G$ is said to be central if $\alpha$ commutes with every inner automorphism of $G$. We construct a family of non-special finite $p$-groups having abelian automorphism groups. These groups provide counter examples to a conjecture of A. Mahalanobis [Israel J. Math., {\bf 165} (2008), 161 - 187]. We also construct a family of finite $p$-groups having non-abelian automorphism groups and all automorphisms central. This solves a problem of I. Malinowska [Advances in group theory, Aracne Editrice, Rome 2002, 111-127].Comment: 11 pages, Counter examples to a conjecture from [Israel J. Math., {\bf 165} (2008), 161 - 187]; This paper will appear in Israel J. Math. in 201

Anion-selective membrane electrodes based on metalloporphyrins: The influence of lipophilic anionic and cationic sites on potentiometric selectivity

The role of lipophilic anionic and cationic additives on the potentiometric anion selectivities of polymer membrane electrodes prepared with various metalloporphyrins as anion selective ionophores is examined. The presence of lipophilic anionic sites (e.g. tetraphenylborate derivatives) is shown to enhance the non-Hofmeister anion selectivities of membranes doped with In(III) and Sn(IV) porphyrins. In contrast, membranes containing Co(III) porphyrins require the addition of lipophilic cationic sites (e.g. tridodecylmethylammonium ions) in order to achieve optimal anion selectivity (for nitrite and thiocyanate) as well as rapid and reversible Nernstian response toward these anionic species. These experimental results coupled with appropriate theoretical models that predict the effect of lipophilic anion and cation sites on the selectivities of membranes doped with either neutral or charged carrier type ionophores may be used to determine the operative ionophore mechanism of each metalloporphyrin complex within the organic membrane phase.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31561/1/0000488.pd

Mechanisms of Nanonewton Mechanostability in a Protein Complex Revealed by Molecular Dynamics Simulations and Single-Molecule Force Spectroscopy

Can molecular dynamics simulations predict the mechanical behavior of protein complexes? Can simulations decipher the role of protein domains of unknown function in large macromolecular complexes? Here, we employ a wide-sampling computational approach to demonstrate that molecular dynamics simulations, when carefully performed and combined with single-molecule atomic force spectroscopy experiments, can predict and explain the behavior of highly mechanostable protein complexes. As a test case, we studied a previously unreported homologue from; Ruminococcus flavefaciens; called X-module-Dockerin (XDoc) bound to its partner Cohesin (Coh). By performing dozens of short simulation replicas near the rupture event, and analyzing dynamic network fluctuations, we were able to generate large simulation statistics and directly compare them with experiments to uncover the mechanisms involved in mechanical stabilization. Our single-molecule force spectroscopy experiments show that the XDoc-Coh homologue complex withstands forces up to 1 nN at loading rates of 10; 5; pN/s. Our simulation results reveal that this remarkable mechanical stability is achieved by a protein architecture that directs molecular deformation along paths that run perpendicular to the pulling axis. The X-module was found to play a crucial role in shielding the adjacent protein complex from mechanical rupture. These mechanisms of protein mechanical stabilization have potential applications in biotechnology for the development of systems exhibiting shear enhanced adhesion or tunable mechanics

Inhomogeneous structure and magnetic properties of granular Co10Cu90 alloys

Granular Co10Cu90 alloys displaying giant magnetoresistance have been obtained by melt spinning followed by an appropriate heat treatment in the range 0-700 degreesC. Their structural and magnetic properties have been studied on a microscopic scale using Co-59 NMR technique and thermoremanent magnetization measurements. The study reveals that in the as-quenched samples Co is involved in two main structural components: small, irregular, strained Co particles (60% of the entire Co population) and a composition modulated CoCu alloy. A high modulation amplitude of the concentration profile in the alloy subdivides the latter in two parts with distinctly different properties. One part consists of ferromagnetic alloy (average Cu concentration of about 20%) with a blocking temperature of about 35 K (involving 6% of the entire Co population in a sample). The other part, containing the remaining 34% of the entire Co population, is a paramagnetic alloy with a blocking temperature below 4.2 K. The ferromagnetic alloy is magnetically soft-its transverse susceptibility is lower by a factor of 7 than the transverse susceptibility of the quenched-in Co particles. The latter population has a blocking temperature of about 150-200 K. During the heat treatment, each of the two main structural components undergoes respective decomposition processes: both of them display two temperature regimes. One process consists in dissolving the quenched-in Co particles after annealing at around 400 degreesC, followed at higher temperatures by a nucleation and growth of the more regular in shape Co particles. The other process resembles a spinodal decomposition of the quenched-in CoCu alloy, resulting in sharpening of the concentration profile and eventually leading to Co cluster formation in samples annealed above 450 degreesC. Both processes end at about T-ap = 700 degreesC, in formation of large, pure Co clusters that are ferromagnetic at least up to 400 K.63

Effects of flavonoids on glycosaminoglycan synthesis: implications for substrate reduction therapy in Sanfilippo disease and other mucopolysaccharidoses

Sanfilippo disease (mucopolysaccharidosis type III, MPS III) is a severe metabolic disorder caused by accumulation of heparan sulfate (HS), one of glycosaminoglycans (GAGs), due to a genetic defect resulting in a deficiency of GAG hydrolysis. This disorder is characterized as the most severe neurological form of MPS, revealing rapid deterioration of brain functions. Among therapeutic approaches for MPS III, one of the most promising appears to be the substrate reduction therapy (SRT). Genistein (5, 7-dihydroxy-3- (4-hydroxyphenyl)-4H-1-benzopyran-4-one) is an isoflavone that has been used in SRT for MPS III. In this report, we tested effects of other flavonoids (apigenin, daidzein, kaempferol and naringenin) on GAG synthesis. Their cytotoxicity and anti-proliferation features were also tested. We found that daidzein and kaempferol inhibited GAG synthesis significantly. Moreover, these compounds were able to reduce lysosomal storage in MPS IIIA fibroblasts. Interestingly, although genistein is believed to inhibit GAG synthesis by blocking the tyrosine kinase activity of the epidermal growth factor receptor, we found that effects of other flavonoids were not due to this mechanism. In fact, combinations of various flavonoids resulted in significantly more effective inhibition of GAG synthesis than the use of any of these compounds alone. These results, together with results published recently by others, suggest that combination of flavonoids can be considered as a method for improvement of efficiency of SRT for MPS III